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Pointwise eigenfunction estimates and intrinsic ultracontractivity-type properties of Feynman-Kac semigroups for a class of levy processes

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posted on 27.05.2016 by Kamil Kaleta, Jozsef Lorinczi
We introduce a class of L´evy processes subject to specific regularity conditions, and consider their Feynman–Kac semigroups given under a Kato-class potential. Using new techniques, first we analyze the rate of decay of eigenfunctions at infinity.We prove bounds on - subaveraging functions, from which we derive two-sided sharp pointwise estimates on the ground state, and obtain upper bounds on all other eigenfunctions. Next, by using these results, we analyze intrinsic ultracontractivity and related properties of the semigroup refining them by the concept of ground state domination and asymptotic versions. We establish the relationships of these properties, derive sharp necessary and sufficient conditions for their validity in terms of the behavior of the L´evy density and the potential at infinity, define the concept of borderline potential for the asymptotic properties and give probabilistic and variational characterizations. These results are amply illustrated by key examples.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

ANNALS OF PROBABILITY

Volume

43

Issue

3

Pages

1350 - 1398 (49)

Citation

KALETA, K. and LORINCZI, J., 2015. Pointwise eigenfunction estimates and intrinsic ultracontractivity-type properties of Feynman-Kac semigroups for a class of levy processes. Annals of Probability, 43(3), pp. 1350-1398.

Publisher

© Institute of Mathematical Sciences

Version

VoR (Version of Record)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2015

Notes

This paper was published in the journal Annals of Probability and the definitive published version is available at http://dx.doi.org/10.1214/13-AOP897

ISSN

0091-1798

Language

en

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